I Know that this equivalence is true, considering the distributivity property of summation:
$$\sum \limits_{i=1}^{N}x_i g_{i,l}\sum \limits_{j=1}^{N}x_j g_{j,k}=\sum \limits_{i=1}^{N}\sum \limits_{j=1}^{N}x_{i}x_{j}g_{i,l}g_{j,k}$$
I was wondering whether there are other properties that would allow me to separate $x_{i}x_{j}$ from $g_{i,l}g_{j,k}$.
